Given $ m \angle AOB = 7x + 30$, and $ m \angle BOC = 4x + 7$, find $m\angle AOB$. $O$ $A$ $C$ $B$
From the diagram, we see that together ${\angle AOB}$ and ${\angle BOC}$ form ${\angle AOC}$ , so $ {m\angle AOB} + {m\angle BOC} = {m\angle AOC}$ Since $\angle AOC$ is a straight angle, we know ${m\angle AOC = 180}$ Substitute in the expressions that were given for each measure: $ {7x + 30} + {4x + 7} = {180}$ Combine like terms: $ 11x + 37 = 180$ Subtract $37$ from both sides: $ 11x = 143$ Divide both sides by $11$ to find $x$ $ x = 13$ Substitute $13$ for $x$ in the expression that was given for $m\angle AOB$ $ m\angle AOB = 7({13}) + 30$ Simplify: $ {m\angle AOB = 91 + 30}$ So ${m\angle AOB = 121}$.